Frequency split suppression of fused silica micro shell resonator based on rotating forming process

Abstract

This paper demonstrates the impact of harmonic error on the natural frequency of micro shell resonator (MSR). Parameterized 3D model is established to analyze the frequency split of resonator with deviation along the circumferential and height direction. Both the n = 1 tilt mode and n = 2 wineglass modes are considered. The simulation results show that frequency split significantly increases as the growth of the 2nd and 4th harmonic errors. At the same time, the influence of frequency split on MSR output is analyzed. The increasing of frequency split will lead to the increasing of quadrature error and decreasing of mechanical sensitivity. The uniformity of the temperature field during processing is considered, a rotary platform is used to reduce the harmonic error of the resonator by improving symmetry of the shell structure. After measurement, the error of 2nd harmonic and 4th harmonic errors have been suppressed by using rotating platform. Finally, more than 10 samples are electrostatically characterized and well matched with the simulation results, the initial frequency symmetry of n = 1 and n = 2 modes is greatly promoted.